Positive Definiteness of High-Order Subdifferential and High-Order Optimality Conditions in Vector Optimization Problems

Abstract

We obtain a new Taylor's formula in terms of the $k+1$ order subdifferential of a $C^{k,1}$ function from $R^n$ to $R^m$. As its applications in optimization problems, we build $k+1$ order sufficient optimality conditions of this kind of functions and $k+1$ order necessary conditions for strongly $C$-quasiconvex functions.